Enhanced Nearby and Vanishing Cycles in Dimension One and Fourier Transform

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-10 DOI:10.4171/prims/59-3-4

Andrea D’Agnolo, Masaki Kashiwara

引用次数: 2

Abstract

Enhanced ind-sheaves provide a suitable framework for the irregular Riemann–Hilbert correspondence. In this paper, we give some precision on nearby and vanishing cycles for enhanced perverse objects in dimension one. As an application, we give a topological proof of the following fact. Let $\mathcal{M}$ be a holonomic algebraic $\mathcal{D}$-module on the affine line, and denote by ${^{\mathsf{L}}}\mathcal{M}$ its Fourier–Laplace transform. For a point $a$ on the affine line, denote by $\ell\_a$ the corresponding linear function on the dual affine line. Then the vanishing cycles of $\mathcal{M}$ at $a$ are isomorphic to the graded component of degree $\ell\_a$ of the Stokes filtration of ${^{\mathsf{L}}}\mathcal{M}$ at infinity.

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一维增强邻近循环和消失循环及傅里叶变换

增强的尾轴为不规则黎曼-希尔伯特对应提供了一个合适的框架。本文给出了一维增强反常对象的附近环和消失环的精度。作为应用，我们给出了以下事实的拓扑证明。设$\mathcal{M}$是仿射直线上的一个完整代数$\mathcal{D}$-模，用${^{\mathsf{L}}}\mathcal{M}$表示它的傅里叶-拉普拉斯变换。对于仿射线上的点$a$，用$\ well \_a$表示对应的对偶仿射线上的线性函数。那么$\mathcal{M}$在$a$处的消失周期与${^{\mathsf{L}}}\mathcal{M}$在无穷远处的Stokes滤波的阶次$\ well \_a$同构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.